Aircraft Performance (lecture 1): Introduction

8/18/2019 Aircraft Performance (lecture 1): Introduction

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AOE 3104 Lecture 1: Introduction

Andy Ko

Aerospace & Ocean Engineering DepartmentVirginia Polytechnic Institute & State University

*Most slides by C. A. Woolsey


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• Dimensions are qualitative, describing essential nature.

• In an MLT system, the four fundamental dimensions are:

Mass [M], Length [L], Time [T] , and Temperature [!]

• Other dimensions are derivable. Examples:

Force [F] = Mass [M] * Acceleration [L T-2]

= [M L T-2]

Speed [V] = Length [L] / Time [T]

= [L T-1]

Dimensions

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•

Units are quantitative, describing amount .

• Two common systems:

• US Customary Units

•

Système International d’Unités (SI Units)

Units

Dimension US Cust. Unit SI Unit

[M] slug kilogram (kg)

[L] foot (ft) meter (m)[T] second (s) second (s)

[!] ºR (ºF + 459.69) K (ºC + 273.16)

4Note: 1 slug = 14.5939 kg; 1 ft = 0.3048 m; 1 ºR = (1/1.8) K


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Units of Force

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•

Units follow standard rules for mathematical composition.

• In an MLT system, the units of force are derived.

US Customary Units:

1 pound (lb or lbf ) = (1 slug)(1 ft/s2

)SI Units:

1 Newton (N) = (1 kg)(1 m/s2)

• These units are “proper” or “consistent.” No “magicconstants” are required to satisfy the physical law: F = m a.

Note: The value and units of a measurement are inseparable:

Length of a Ruler : 12 in = 30.48 cm = (1/660) furlongs


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Force vs. Mass mixup

•

Force and mass are not interchangeable – Mass is a measure of an object’s material

• Units: slugs, kilograms

– Force is the influence that tends to change the motion

of an object• Units: Pounds, Newton

• Pounds-force vs Pounds-mass

– 1 lbf = 1 slug * 1 ft/s2 = 1 lbm * 32.2 ft/s

2

–

So, 1 lbm weights 1 lbf on earth• lbf = 32.2 lbm-ft/s

2 = slug-ft/s2

– Confusing, isn’t it?

• Stick with lbs for force, and slugs for mass "

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Why pay attention to units?

•

Consistent frame of reference

•

Lessons from not paying attention to units

– Mar Climate Orbiter, September 1999, $125

million – Air Canada 143, Boeing 767, July 1983

•

Ran out of fuel in-flight

– Korean Air 6316, MD-11 freighter, April 1999

•

8 killed, 37 injured

7

A foolish man never learns from his mistakes. A goodman learns from his own mistakes, but a wise man

learns from the mistakes of others.


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Body & Inertial Frames

8Note: Attitude angles are not really measured about the body axes. More in AOE 3134...

Coordinate system is aligned with aircraftplane of symmetry


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Wind Frame

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Angle of Attack:

Angle of Sideslip:


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Particle Representation

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Newton’s 2nd Law of Motion:

Alternatively:


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The Forces

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Newton’s 2nd Law of Motion:So what is F ?

• Externally generated fluid forces (aerostatic & aerodynamic)

•

Internally generated fluid forces (propulsion)• Gravitational forces

• Ground contact forces

Image: Albequerque Intl Balloon Fiesta

Aerostatic Forces Aerodynamic Forces

Image: NASA

Image: Boeing

Ground Contact ForcesPropulsion Forces

Image: Pratt & Whitney


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Aerostatic Force

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Aerostatic force may be computed from Archimedes’ principle:

Image: Albequerque Intl Balloon Fiesta

Comments:• Most easily expressed in the inertial frame.

• Significant for “lighter-than-air (LTA)” vehicles.

Image: Goodyear

F aerostatic

=! ! gVol( ) z I


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Aerodynamic Force

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The three components, resolved in the wind frame, are:

Drag:

Side Force:

Lift:

Comments:• Most easily expressed in the wind frame.

• Depends on fluid properties, vehicle geometry , andvehicle motion relative to the fluid.

! D x w

!SF yw

!

L z w


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Propulsion Force

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Assume that propulsion acts in aircraft plane of symmetry:

Comments:

• Most easily expressed in the body frame.

•

Performance characteristics depend greatly on propulsion.


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Gravitational Force

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Comments:

• Most easily expressed in the inertial frame.

•

Can change significantly over the course of a flight.

Image: USAF

The gravitational force is simply the vehicle’s weight:

F gravitational = m g( ) z I


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Ground Contact Force

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Comments:

•

Most easily expressed in the inertial frame.

• Important for computing takeoff and landing distance.

Image: Boeing Image: USN

Neglecting cross-winds, ground contact force is:


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Types of Motion

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Symmetric Motions: Motions in the inertial plane definedby the aircraft plane of symmetry, in wings level flight.

• Examples:

–

Wings-Level Cruise

– Wings-Level Climb/Descent

– Take-off & Landing

• Asymmetric Motions: “Out of symmetry plane” motions.

• Examples:

–

Banked turns –

Rolls

– Sideslipped landings

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Trajectory Equations

(Symmetric Flight)

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Comments:

• To assess performance, must know how T, L, and D vary.


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Density

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Definition: The density ( !) of a substance is the mass ofthat substance per unit volume.

Density is a scalar field. (It varies with location.)

Consider a differential volume element, with differential mass.

Assuming the fluid is a continuum:


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Temperature

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Definition: Temperature is a measure of the averagemolecular kinetic energy.

Temperature is a scalar field.

High TemperatureLow Temperature


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Pressure

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Definition: Pressure is the normal force exerted on asurface (physical or otherwise) per unit area.

Pressure is a scalar field.

Consider a differential area subject to a normal force.

Assuming the fluid is a continuum:


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Velocity

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Definition: Fluid velocity is the rate of change of positionof an infinitesimally small fluid element at a point.

Velocity is a vector field.


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Fluid Flow Field

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Ideal Gas Law

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Definition: An ideal gas is one for which intermolecularforces are negligible.

Equation of State for an Ideal Gas:

where R is the specific gas constant.

For air:

P = ! RT

R =!

M =

8314 J / kg !mole !K ( )28.96 kg / kg !mole( )

= 287.1 J

kg !K

=1716 ft ! lb

slug ! R


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Some Other Fluid Properties

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Viscosity (µ): Ratio of shear stress to velocity gradient for aNewtonian fluid.

Specific Heat at Constant Pressure (cp): Ratio of heatadded to temperature increase, at constant pressure.

Specific Heat at Constant Volume (cv): Ratio of heat addedto temperature increase, at constant volume.

Ratio of Specific Heats*:

Speed of Sound:

Objective: Relate flow characteristics, including fluidproperties, to forces so we can assess performance.

*For air, the ratio of specific heats is 7/5 (or 1.4).

! = cP

/ cV

a = ! RT


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What next?

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Hydrostatics and the Standard Atmosphere.

Week #2 Reading:

•

Anderson: Sections 2.1-4, 3.1-5, and 4.1-11• Optional: Watch Nova: Battle of the X-Planes

• http://www.hulu.com/watch/23356/nova-battle-of-the-x-planes

Homework : Will be posted today by 5pm

Documents

Aircraft Performance (lecture 1): Introduction